Algebraic geometry in positive characteristic presents a rich and intricate landscape where classical techniques meet novel challenges associated with fields of prime order. This area synthesises ...

Let 𝓧 be a complex projective manifold of dimension n defined over the reals, and let M denote its real locus. We study the vanishing locus Z s d in M of a random real holomorphic section sd of 𝓔 ⊗ ...

Algebraic and differential geometry stand as two intertwined pillars of modern mathematics. Whereas algebraic geometry investigates the solution sets of polynomial equations using the refined language ...

Both algebraic and arithmetic geometry are concerned with the study of solution sets of systems of polynomial equations. Algebraic geometry deals primarily with solutions lying in an algebraically ...

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of recent work by the ...

The drive to get every student to take so-called college gateway courses has succeeded, a new federal study finds, but students taking Algebra 1 and Geometry classes are getting considerably less ...